Multiple flight course second order missile programmer



Feb. 16,' E65 a. H. scHRoADER ETAL MULTIPLE FLIGHT COURSE SECOND ORDER MISSILE PROGRAMMER N .bm

AGENT Feb w65 n. H. scHRoADER E'rAn.. 3,159,72?

PROGRAMMER MULTIPLE FLIGHT couRsR sRcoND ORDER Mssm: Filed June 23. leso N Sk Feb. 16, 1965 l. H. scHRoADER ETAL 3,169,727

MULTIPLE FLIGHT COURSE SECOND ORDER MSSILE PROGRAMMER Filed June 23. 1960 7 Sheets-Sheet 5 Feb. 16, 1965 l; H. scHRoADE-R r-:TAL 3,E69,727

MULTIPLE FLIGHT COURSE SECOND ORDER MSSILE PROGRAMMER Filed June 2 3. 1960 7 Sheets-Sheet 4 @QRS QH van LJQ k Feb. 16,1965 1. .scHRoADER ETAL 3,159,727

MULTIPLE FLIGHT COURSE SECQND ORDER MISSILE PROGRAMMER Filed June 25. 1960 7 sheets-sneer s Feb. 16,1965

3,169,727 l MULTIPLE FLIGx-i'rv coURsg sEcoND ORDER MIssILE PROGRAMMER Filed June 25.- 1960 l. 4H. scHRQADER ETAL 7 Sheets-Sheet 6 NGN Feb. 16, 1965 H. scHRoA'DER v:a1-Al. 3,159,727-

MULTIPLE FLIGHT COURSE SECOND ORDER MISSILE PROGRAMMER Filed June 23, 1960 7 Shets-Sheet 7 bm. SG ESQ United States Patent O 3,169,727 MIHJTIPLE FLIGHT COURSE SECOND (DEBER lVIlSSlLlE PRGRAMMER Irvin H. Schroader, Simpsonville, and Melvin E. Hosea and Leo C. Miller, Silver Spring, Md., assignors to the United States of America as represented by the Secretary of the Navy Filed dune 23, 1969, Ser. No. 38,408 1 18 Claims. (Cl. 244-14) The present invention relates generally to improvements in missile guidance systems and the like and more particularly to a new and improved missile guidance sys- .tem for beam-riding missiles wherein a single guidance system is adapted for quick changeover from'one 'midcourse missile guidance program to any one of a plurality of other such programs in accordance with missile requirements and target considerations, all suchguidance programs being so suited to their specied conditions of operation as to minimize missile fuel consumption, insure maximum missile range, and provide continual variation of the guidance system sensitivity of the missile inA accordance with maximum target kill probability.

In the field of missile guidance system development, it has been the general practice to employ ground computing devices in conjunction with cooperating guidance transmitters to guide various beam-riding missiles to their targets. Although such devices have generally served their purpose, they have not proved entirely satisfactory under al1 conditions of service and operation for the reason that considerable difficulty has been experienced in minimizing the deleterious effects of noisy radar input data upon both the computer and resulting programmed missile trajectory, with subsequent effects upon missile fuel consumption, missile range, and probability of collision of the missile with the target. Hence,.those concerned with the development of missile guidance systems have long recognized the need for a guidance system capable of Such wide adaptability as to enable rapid and precise changeover from one type of mid-course missile guidance program to some other mid-course program,-

which might be made dependent upon any desired set of input parameters such as range, angle, or a combination thereof, and which would simultaneously avoid all of the foregoing difficulties commonly encountered by such systems.

An additional critical problem confronting those who devise such missile guidance systems has been the almost universal quest for a versatile programming system capable not only of Yacting upon any desired combination of input parameters but of manipulating such data in accordance with basic master programming equations to effect proper approach of the position coordinates of the missile to those of the target in a manner which would assure maximum missile range, minimum missile fuel consumption, and greatest probability of target kill. The present invention fulfills all of these needs.

The general purpose of this invention, therefore, is to provide a multiple flight course missile programmer which embraces substantially all of the advantages of previously employed missile guidance systems and yet possesses none of the aforedescribed disadvantages. To attain the latter, the instant invention contemplates,

`among other things, provision of amultiple Hight trajectory missile programming system capable of guiding beam-riding missiles along prescribed trajectories most suited to considerations of missile performance characteristics and target threat, and which will perform in a manner insuring maximum eiciency through the smoothing of input radar data, in the computing stages of the programmer itself, thereby minimizing the effects of noisy output information upon missile servos. The latter smoothing effect upon output information to the guidance transmitters is continued until the missile is within close striking range of the target and serves to minimize drag on the missile caused by wing vibration and subsequent high resistance to air iiow while the missile is in Hight.

The missile guidance system of the instant invention further contemplates the provision of a novel second order programmer computing section which acts upon input data so as to cause the elevation and azimuth of the guidance transmitter to approach the elevation and azimuth of the target, before target intercept, in accordance with a prescribed second order generalized system equation, the constants of the latter equation and the input data to said computing section being chosen to suit the characteristics of the missile being fired and the desired Hight course program to be followed. In this manner, the novel missile programmer of the instant invention provides a computing section for realizing a plurality of varied flight trajectories which may be made angle dependent, range dependent or dependent upon any other desired set of input parameters. The latter novel and inventive computing section is thus extremely well adapted to the fulfillment of all necessary guidance requirements.

Accordingly, an object of the present invention is the provision of a new and improved missile guidance system.

Another object is to provide a new and improved missile guidance system capable of quick changeover from one mid-course guidance program to another.

A further object of the instant invention is the provision of a novel missile guidance system capable of quick changeover from one mid-course guidance program to another and which may be made dependent upon any desired set of input parameters.

Still another object resides in the provision of a new and improved missile programmer which minimizes missile fuel consumption, increases missile range, and insures maximum probability of target kill.

Yet another object of the instant invention is the provision of a new and improved missile programming device capable of causing missile position data to app-roach target position data in a preferred manner to effect maximum efficiency and probability of target kill with minimum drag upon the missile during flight.

A still further object of the persent invention resides in the provision of a new and improved missile guidance system which prevents banging due to noisy guidance information data and consequent damage to missile wing flaps and missile servos.

Another object of the persent invention is to provide a novel multiple flight course missile programmer assuring guidance ight trajectories with increased fuel economy and improved accuracy.

A still further object of the present invention is to ice provide a new and improved missile guidance system capable of variable guidance sensitivity during mid-course missile guidance and wide adaptability to a great variety of programmed ight trajectories.

It is a still further object of the instant invention to provide a new and improved missile guidance system of such versatility as to be adaptable to missiles which are totally beam-riding, namely those which ride the guidance beam from guidance initiation 'to the point of actual target collision, and also to missiles which are only partially beam-riding, in that they ridethe guidance beam only until they approach the vicinity of the target.

Other objects and many of theattendant advantages of this invention will be readily appreciated as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:

FIG. l is a schematic representation by block diagram proper position.

of a complete missile guidance and control system constructed in accordance with the instant invention;

FIG. 2 is illustrative of a missile riding a guidance beam to a designated target and defines some of the symbolism to be used for various parameters subsequently set forth in the specification;

FIG. 3 illustrates the axes of motion for a typical three coordinate tracking radar system utilized in conjunction with one embodiment of the instant invention;

FIG. 4 illustrates geometrically the conversion of three coordinate information from the tracking radar system shown in FIG. 3 to equivalent two coordinate information form;

FIG. 5 is a schematic representation by block diagram of a complete missile flight course programming computer in accordance with the instant invention;

FIGS. 6 and 6a illustrate typical circuit embodiments of a complete missile programming computer in accordance with the present invention, including both the input and output data sections;

FIG. 7 illustrates a novel second order missile programmer computing circuit in accordance with the instant invention;

FIG. 8 illustrates a servo system arrangement typical of those utilized in conjunction with the missile guidance system of the instant invention;

FIGS. 9 and 10 are illustrative of programmed missile flight trajectories obtainble in accordance with one embodiment of the instant invention; and

FIG. 11 is a graph illustrating the manner in which guidance sensitivity may be varied in accordance with one embodiment of the present invention.

The multiple flight course second order missile programmer of the instant invention comprises basically a new and improved electronic analog computer in com- CFI bination with a series of servo systems and working with necessary input and output radar systems, including the power, cabling and switching necessary to implement the latter. The resulting system is 'thereby rendered capable of accepting radar data in synchro form and,

tronic analog programming computer section 'to provide l the required missile flight program in accordance with prescribed trajectory equations to be hereinafter more fully described. Furthermore, the system, as disclosed in the illustrated embodiments, is also capable of converting the computed ight program, in both azimuth and elevation, from the conventional D.C. signal output information form emanating from the computer into synchro data form which may then be conveyed to the guidance transmitter radars to command the latter into The guidance system concept of the instant invention may also be readily presented, among its many practical embodiments, in such a manner as to facilitate interchange or cross-connection of its components, servos and computing amplifiers to provide a great variety of different trajectory Fright programs depending upon specitic operational and performance characteristics of the missile to be iired and various target considerations. Such a system may also be utilized to provide a substantial variety of post intercept programs. In practice, the flexibility of these units is even further enhanced through the wide use, wherever possible, of multiple patch panels, the latter being classified in accordance with functions handled, such as synchro data,

VDC. functions, etc.

t target, the missile be caused to intercept the target in a maneuver within the acceleration capabilities of the missile to produce either a target hit or a near miss and thereby destroy the target.

The instant invention contemplates the manipulation of various input data in accordance with generalized system equations, the constants of which are chosen in accordance with missile characteristics and target considerations to bring the missile to its target in the prescribed manner. A computing system, in accordance with the present invention, for accomplishing the latter will perform the same series of functional operations upon any and all input data irrespective of whatever parameters such input data may represent. Therefore, a great variety of Hight programs are made possible for any given missile through the programming system of the instant invention merely by varying the nature of the input data and constants for the generalized system equation manipulations in the programming computer section.

By way of example, two types of programmed trajectories within the scope of the instant invention will be described. The-two sample llight programs illustrated will be designated type A and type B. The type A program is specifically designed for use with missiles which are pure beam or totally beam-riding, that is missiles which ride guidance beams all the way to their respective targets, whereas the type B program is primarily adapted for use with a partially beam-riding missile which rides a guidance beam only to within close proximity of the target and thereafter homes in on the target by means of guidance devices which may be wholly within the missile itself and independent of any ground control.

Referring now to the drawings, which illustrate one embodiment of the instant invention, there is shown in FIG. l a schematic representation by block diagram of a complete missile guidance system which, in accordance with the instant invention, is capable of switching from a iirst mid-course guidance program such as type A, to a second mid-course guidance program such as type B, the characteristics of the latter guidance programs to be subsequently more fully described.

FIG. l shows a search radar 20, incorporating a separate height finder 2l, which sends out a radar search beam i3 to a target l2 and in turn receives a reiiected signal i4 from the target. Many types of Search radar instrumentation are suitable for utilization in carrying out the latter function, including search radars having built in height Y nders or those which incorporate such units separately. The output of the search radar 2@ and height iinder ai consists of information relating to rough values of target azimuth and range and an even rougher value of target elevation. The latter output -data is then conveyed as input information to a tracking radar 22, which may take a great variety of forms but which will be here illustrate as incorporating a three-coordinate system utilizing train, traverse, and elevation axes, the actions of cach of which will be hereinafter more fully described.

The target azimuth, target range and target elevation information from the search radar 2f@ and height finder 21 enables the operator of the tracking radar 22 to either actually lock on the target l2 or to throw the tracking radar into searc operation, which is essentially a scan raster of plus or minus a discrete number of degrees about a position which is believed by the operator of the tracking radar 22 to be the approximate target position as indicated by the rough information received from the search radar system. Other modes of radar systems feeding the tracking radar 22 might include such systems as the Air Force SAGE type concentrated network of defense radars to provide input datato the tracking radar system.

The tracking radar 22 transmits its own radar beam i5 to the target l2 and receives a reflection le therefrom. The output data from the tracking radar Z2. consists of target elevation, target train, target traverse, and siant rang-e from the tracking radar 22 to the target i2. The

latter output information from tracking radar 22 is derived for further use through synchro devices physically located at the tracking radar unit itself. Shaft rotations about the various axes of the tracking radar 22 are converted by means of such synch-ro devices to synchro signals, threewire lines being conventionally embodied for each synchro, to provide outputs from each synchro which are directly proportional to the number of degrees of radar shaft rotation from an established Zero reference position.

The synchro output data from the tracking radar 22 is in turn fed to a computer section 23 of the instant invention. The latter tracking radar data is first directed to the input converter servo section 24 of the computer 23 wherein the synchro input information is converted by means of Servomechanism devices to electrical signals in the form of D.C. voltages proportional to the original radar shaft rotations from which the input synchro signals were derived. Such DC. voltage signal form is required for use by the programmer section 25 of the computer 23. The programmer section Z5 utilizes the latter D.C. voltage outputs of the input converter servos as electrical voltage inputs to a computing section which manipulates such input voltages on the basis of prescribed generalized trajectory equations, and produces D.C. output voltages which are then fed to an output converter servo section 26.

The output converter servo section 25 of computer 23 reconverts the D.C. output voltage signals from the programmer section 25 to synchro signal output form for transmission to and utilization by the guidance radar transmitters denoted generally as 27 in FIG. l ofthe drawings. The latter guidance radar transmitters 27 can be physically located near the tracking and Search radars 22 and 20, respectively, or at least within a few hundred feet vof the -tracking radar to prevent the introduction of severe parallaX errors; the distance to the search radar not being as critical.

The guidance radar 27 transmits a radar signal 17 to the missile 19, but only in a single direction, that is, guidance radar 27 receives absolutely no reflected signal from the missile. The major distinction'between the guidance radar 27 and the tracking radars are that the guidance radar is commanded into position by the output elevation and azimuth signals from the ground computer section 23. In the illustrated embodiment, however, the guidance radar transmitter does track in range on the type fA program. In contrast to the operation of tracking radar 22, the tracking accomplished by the guidance radar is not carried out by receiving a signal from the missile constituting a reflection of an original signal generated in the guidance radar itself. On the contrary, missiles utilizing the type A program trajectory carry a beacon 28 incorporated into the missile and which is triggered by the guidance beam 17 from the guidance radar 27 to generate a beacon signal 18 of its own. The latter beacon signal 1S is directed from the missile 19 to the guidance radar 27, the time of delay of the arrival of the beacon signal` at the guidance radar being a measure of the slant range to the missile.

For the type B program, which is designed for utilization solely by missiles which incorporate separate homing systems, the program flight trajectory is not dependent -upon input information to the computer section 23 relating to the difference between target slant range and missile slant range, and hence, the guidance radar 27 is not required to track in range for such a program.

For the type A program, therefore, the missile slant range information received by the guidance transmitter 27 is fed back into the tracking radar 22 to enable the latter unit to direct an output to the computer section 23 which is the difference between slant range to the target and slant range to the missile, whereas for the type B program, with homingj there is no tracking in range by the guidance radar 27 nor any feedback of such information from the guidance radar 27 to the tracking radar 22, and, therefore, in the latter instance, the output of the tracking radar is simply slant range to the target.

Missiles utilizing the multiple flight course programmer of the instant envention must, of necessity, be beam riders. Such a missile is captured by the radar beam 17 emanating from the guidance transmitter 27 so that the missile 19 is caused to follow the beam as the beam moves in accordance with the programmed flight trajectory equation. Servomechanism devices within the missile 19 itself steer the missile in accordance with the transmited guidance signals so that the missile is caused to always remain within the guidance beam after capture, provided the guidance beam moves in such a manner that the missile capabilities of linear velocity and lateral acceleration are not exceeded.

In actual operation, before launching, the operator elects in accordance with the nature of the missile to be fired, either the type A or type B program trajectory. The operator then proceeds to flip various switches in the guidance radar, eg., for tracking in missile range or not, and simultaneously operates switches in the programmer section 25 of the computer 23 to select proper constants and input data channels for the chosen program.

Synchro data form is utilized for accurate transmission of data between the input radar system 22 and the computer section 24 as well as between the computer section 26 and the output guidance radar transmitters 27. Stich synchro output is utilized primarily because of the required maintenance of transmission precision, namely minimal line losses, over long distances, particularly those in excess of feet. Another reason for using synchros is to enable a system of multiple speeding facilitating transmission of data utilizing two synchro inputs. In one embodiment of the latter arrangement, a pair of synchros may be provided with one synchro turning at a 1:1 speed ratio and the second rotating at a 36:1 speed ratio such that the first synchro turns a full revolution for 360 degrees while thesecond turns one revolution for every l0 degrees of rotation. Such a dual speeding arangement enables finer precision of reading angles.

As outlined above, several instances arise in the missile programming apparatus of the instant invention wherein a shaft rotation or a voltage must be converted into some other information form. The most common device utilized for accomplishing such conversions is the servof Referring to FIG. 8 of the drawings, a servo, for purposes of the present discussion, is considered to be a unit comprising an input converter device 30, a servo amplifying device 31, and a servo motor 32 incorporating a follow-up feedback system 33 to the input converter 3th. In general terms, the output voltage 0o introduced by the follow-up system 33 into the converter 30 is substracted from the input command voltage 01 to the input converter 30 to produce an error signal e which, upon amplification by the servo amplifier 31, causes the shaft of the servo motor 32 and incorporated follow-up system 33 to rotate in such a direction as to reduce the error voltage e to zero, thereby establishing a null position of the servo mot-or shaft. The resulting equilibrium shaft position of the servo motor 32 is thus directly proportional to the command voltage 0,. The latter shaft position can be used as such, or converted to a proportional voltage, either A C. or D.C., by means of an electrical output converter' 34 generally consisting of a suitable potentiometer arrangement, as will be further illustrated in connection with the programming computer circuitry to be hereinafter more fully described. The purpose therefore of a position servo is to cause an output member, such as the shaft of servo motor 32, to follow the position of a possibly remote input shaft or member.

Briefly, synchro devices suitable for use with the device of the instant invention essentially comprise trans- Ti formers having single rotatable windings. Synchro transmitters, synchro differentials and synchro control transformes are of interest in connection with the instant invention.

A typical synchro transmitter will have a rotor winding, excited by some A.C. voltage reference, which may be 115 volts or the like, and which is continuously rotat'able through 360. Three stator windings are electrically spaced at 120 intervals in the outer shell of such a transmitter with a single side of each of the stator windings in common. As a result, the voltage induced in each stator windings is a unique function of the rotor position of the` transmitter. These three voltages may be transmitted by means of a conventional three-wire synchro transmission system over distances of considerable magnitude without deterioration in accuracy, since it is principally required only that relative balance be maintained, that is that the ratios of the various stator voltages to each other be maintained constant, there being no requirement that the absolute magnitude of the latter voltages be also maintained constant. Therefore, since each of the three synchro transmission lines will have the same loss characteristics, relative losses will be cancelled.

The three synchro leads lfrom the stators of the synchro transmitter are terminated at the corresponding three stators of a control transformer in the input converter servo section 24 of the computer 23, the latter control transformer being similar in structure to that of the synchro transmitter, although electrically some minor differences obtain. The rotor winding of the control transformer will have a voltage induced in it until it has been rotated to exactly the same relative position as the rotor of the synchro transmitter. Over a considerable angular displacement, an error voltage proportional to the angular misalignment between the rotor of the control transformer and the rotor of the synchro transmitter will be produced, so that the control transformer thereby serves as a differential device for producing an error voltage which may be then directed to a servo amplier such as amplifier 31 shown in FIG. 8 of the drawings.

On occasion, in the device of the instant invention, it is necessary to obtain in synchro form a quantity representing the addition of two shaft rotations. The latter may be accomplished by means of a synchro differential inserted between the synchro transmitter and the synchro control transformer. The three output leads from such a synchro differential will carry voltages which will be the same as those that would be produced by the synchro transmitter if the rotor shaft angle of the synchro transmitter were increased by the angular rotation given the synchro differential.

The error voltage derived from the control transformers must receive voltage and power amplification before a servo motor, such as the motor 32 shown shown in PEG. 8, can be successfully operated from it. ln the vicinity of a null or zero error rotor position the output from a typical control transformer, as used in the illustrated embodiments of the instant invention, is of the order of one volt per degree of error. A good synchro servo should lbe capable of acting on an error as small as 0.0l, represented by an error signal output voltage of l millivolts, and yet still turn out three volts to the servo motor. Therefore the servo amplifier utilized with such a control transformer must have a voltage gain of approximately 300, and should be capable of supplying about watts of power where a large rotor error signal calls for high velocity slew to a new position. The servo motor driven by the output of the servo amplifier in turn drives the control transformer via the follow-up system 33 and through appropriate gearing so that a null position of the control transformer rotor is finally realized.

The essential functions of the synchro servo system, as described above, is to serve as a data receiver and converter for distant radars or guidance transmitters such as those shown in FIG. 1 of the drawings. In such instances, the servo motor of the synchro servo device drives one or more precision wire-wound potentiometers which serve to convert the rotor shaft position of the input converter or control transformer into an accurately proportioned voltage. In some cases, auxiliary devices, such as ball and disc integrators, trigonometric functiontapered potentiometers or A.C. resolvers are also driven as may be required for desired conversions in any specific situation. In any case, the output conversion voltages so derived may be then passed into the `computer section for further manipulation in accordance with prescribed equations.

Since the accuracy of the typical single synchro is generally only eight minutes of arc, then, as previously set forth, the single speed synchro servo device shown in FIG. 8 of the drawings and described above may prove insuiiciently accurate for many purposes. ln actual practice, therefore, two synchro transmitters and two synchro control transformers are used in a one and 36 speed combination. Thus, the error voltage is derived from a control transformer making one revolution per 10 of the incoming data. lf the servo falls into error greater than 2, a two-speed mixer is utilized to switch control to the one-speed control transformer to prevent the settling on a false null every ten degrees.` in such dual speed data systems, an ambiguous zero is found to exist at those values of the transmitted variable which require an even number of rotations of the high-speed synchro and an integral number of half revolutions of the low-speed synchro. The problem of this ambiguous zero can be solved by inserting in series with the error voltage from the one-speed synchro control transformer what is commonly referred to in the art as a sticko voltage. The purpose of the latter stickoff voltage is to displace the false zero of the one-speed system so that there is enough voltage from the one-speed system to drive the servo motor away from what was the ambiguous zero. Such a method of utilizing a stickofi voltage in a dual-speed synchro system is Well known in the art, and the equations for the required stickotf voltage needed with any particular dual-speed synchro data system are to be found in the Mlfl". Radiation Laboratory Series, vol. 25, Theory of Servomechanisms, pages -88.

For internal data transmission, analog voltages within the computer section of the missile programmer of the instant invention may be carried by means of cables over reasonable distances, providing proper precautions are taken to provide adequate shielding and thereby avoid or minimize ground current loops.

FIG. 3 of the drawings depicts in diagrammatic form the arrangement of the various axes of a three-coordinate tracking radar system 22 such as that utilized in the cornplete guidance system shown in FG. l. The three-axis system illustrated in FiG. 3 includes a train or azimuth axis 3l which is perpendicular to the horizontal or ground reference plane and an elevation axis 32 parallel to the ground reference plane. Rotation about the elevation axis 32, therefore, is always in a plane which is perpendicular to the ground plane. A traverse axis 33 is also provided in the system 22, the traverse axis 33 being permanently afhxed to the elevation axis 32 so that the traverse axis pivots with the latter in the vertical plane. Thus, rotation about the traverse axis 33 will always lie in a plane intermediate the ground reference plane and a vertical plane. Although it would be possible to align the tracking radar unit 22 to any position merely by rotation about the train and elevation axes alone, the traverse axis 33 is included, to enhance the versatility of such tracking radar units by increasing their ability to track rapidly moving targets which may pass directly overhead. Normally, once the elevation and train axes, 37. and 3l, respectively, have been rotated to specific positions to enable tracking of a point following a trajectory in a transverse plane, that is, one intermediate the vertical and horizotnal planes, it would be necessary to simultaneously continue rotation of bothrhe train and elevation axes if the system 22 were to successfully follow the motion of the target while it remained in such a transverse plane. However, where a traverse axis such as 33 is employed, the train and elevation axes 31'and 32 need be utilized merely for initial alignment of the radar 22 with the target. Thereafter, as long as the target is constrained to motion in the same transverse plane, the radar 22 can follow the target simply by sweeping about the single traverse axis 33. Such radar system arrangements have found extremely wide use on shipboard where enemy planes may frequently come in low and -fast directly overhead, causing extreme diiculty Where accurate tracking necessitates radar rotation about more than a single axis.

The use of the three-axis radar system`22 described above, though vastly improving tracking capabilities for rapidly moving targets, does however introduce some complications insofar as the simplification of input information to the programming computer is concerned. It is desirable, therefore, to reduce the target position data emanating from the tracking radar Z2 from a threecoordinate system to a two-coordinate system before introduction to the computer section 25.

Elevation angle 6E is unaffected by the existence of a traverse axis. However, rotation about the traverse axis 33 does produce a reected change in the horizontal or train plane. FIG. 4 of the drawings illustrates the conversion of traverse angle readings into the ground or train plane. It will be evident from FIG. 4 that the traverse angle reading @Tv can be reflected into the train plane simply by dividing the traverse angle by the cosine of the angle of elevation E or, in other words, multiplying the traverse angle @TV by the secant of the angle of elevation. The latter condition may be expressed as follows:

AT=TN+TV SeC ET where AT=Azimuth of target in degrees TN=Train angle of target in degrees Tv=Traverse angle of target in degrees ET=Elevation angle of target in degrees F :Firing G=Guidance program initiation (capture of missile by guidance beam) P= Present time :Intercept of target by missile The system of indicating angles and ranges employs subscripts in a slightly different manner. Basically, the irst subscript indicates the equipment or place which is under consideration. The second subscript indicates the time which is pertinent. However, for simplicity, the time symbol subscript P (present time) is omitted Where no confusion would result. Therefore, the necessary symbols for the ensuing discussion are set out below:

AGp=AG=Azimuth of guidance transmitter at present time AGG=Azimuth of guidance transmitter at guidance initiation I E=Program constant, elevation D12 =Target slantJ range rate =Missile slant range rate i KAzProgram constant, azimuth wnzGain sensitivity factor for second order missile programmer computing circuit dan nda TPI=Time from present to intercept e=Output data from second order computing circuit elzlnput data to second order computing circuit eE=(eO-ei) For elevation computing circuits eA=(e-ei) For azimuth computing circuits c=A constant Havingthus ,described the symbolism to be utilized in the accompanying description, the operation of the second order missile programmer of the instant invention will now be more fully detailed.

As previously outlined, typical requirements for a modern guided missile are that the missile be tired at a relatively high launcher elevation angle, rapidly ascend to a high altitude, cruise as long as possible at this altitude for maximum ramjet engine efficiency, and then dive towards the target in a maneuver within the acceleration capabilities of the missile, to produce a target kill. Two types of trajectories, suitable for these purposes, have been evolved and will be described. These two types of trajectories have been previously referred to as the type A and type B programs,.the type A program being designated for a totally beam-riding missile carrying a beacon capable of relaying missile range information to the guidance transmitter, and the type B program being for partially beam-riding missiles, without beacons, which utilize separate homing systems to intercept the target. The general theory of operation of the type A and type B Aprograms will be made clear by the following analysis.

After the missile is initially fired at a relatively high launcher angle, a discrete period of time elapses before capture of the missile by the guidance beam is accomplished. Thereafter, EG, the elevation of the guidance transmitter, must approach ET, the elevation ofthe target, at such a rate that the above stated trajectory and flight conditions are fullilled, that is, EG-ET must change in a proper manner in accordance with prescribed programming equations as will be set out below. FIG. 9 of the drawing illustrates the form of EG-ET found desirable in the instances where the type A and type B programs are utilized. The resulting midcourse missile flight trajectories are shown for these programs in FIG. 10 of the drawings. It will be noted from FIGS. 9 and 10 that, whereas the type A program causes the missile to dive on the target in a direct collision course, the type B program causes the missile to approach asymtotically to the line of sight from the 4tracking radar to -the target prior to collision.

The type A program is the more accurate of the two types of flight programs illustrated. Although the generalized system equations for both the type A and type il B programs are similar, in accordance with the instant invention the type A program trajectory is varied from Vthat of the type B program by varying the nature of the parameters which are fed into the computer section as -input data.

The type A program with its direct intercept collision course is generally chosen for multiple targets and Wherever the potential thereat is very great, as where the target may be carrying a thermonuclear device. On the other hand, the type B program trajectory is usually chosen only for single targets or for minimal multiple target threats since, as previously pointed out, the type B program contemplates a homing-type of asymtotic collision course, such homing systems being susceptible to serious confusion where multiple targets are engaged.

For the purpose of analyzing and specifying missile performance, as controlled and guided by the novel programmer of the instant invention, it is necessary first to dene the ight trajectories, as represented by the output data from the computer section, in terms of specic mathematical system equations and specied input parameters to the computer section utilizing the latter equations. The generalized system equations utilized by the programmer of the instant invention contemplate second order differential solutions by the computer section. Thus, the novel programmer performs in accordance with the equation where eo represents the generalized system equation, the variation of the constants and input data of which enables the Wide variety of programs obtainable with the instant invention. The second order system equation is expressed in terms of o rather than e0 form for sake of simplicity as will subsequently be made evident. Thus, the behavior of the second order equation computing circuit, as contemplated by the instant invention, may be uniquely described in terms of the following generalized system equations.

Equation 3 yields t=P o= Zone L G (wnz-ldin) edt-iconstant (5) An important feature of the circuitry utilized for computing the various program trajectories in accordance with the above equations is the manner in which the value of wn, the gain sensitivity factor, is varied. A low value of wn allows e0 to change only slowly and to be relatively insensitive to changes in ei, the input data. On the other hand, a high value of wn allows eo to change rapidly and to be more sensitive to tluctuation in ei. Therefore, the manner in which wn, the gain sensitivity factor, is programmed is a major aspect of the instant invention.

It has been determined empirically, in accordance with this invention, that adequate smoothing of noisy input data and desired flight trajectory accuracy will be realized if the gain sensitivity factor, wn, is programmed in accordance with the equation wn TPI-t6 (6) where Tpztime from present to intercept. Such an empirical programming equation for wn insures values of gain sensitivity lying between zero and unity and eliminates the situation where a gain sensitivity of infinity would be required, the latter case being one which would obtain if the gain sensitivity constant c were omitted from Equation 6.

muze dt -I- constant where Equation 10 represents the master generalized system equation for the missile programmer of the instantinvention.

The empirical relation for on from Equation 6 may be placed in more suitable form for handling by the computer section as follows:

Tp1=ti1ne from present to intercept and since A. distance tune velo city therefore TPI slant range difference between missle and target slant range rate difference between missle and target to a very close approximation. Hence, Equation 6 becomes The instant invention utilizes the Equation l2 form of on in the Equation 1'0 form of the master generalized program equation, the computer circuitry of the instant invention being set up to solve Equation l() with the value of the gain sensitivity factorwn, varying in accordance with Equation 12. The various constants in Equations l0 and '12 are chosen to tailor the output flight trajectories from the computer section of the programmer in accordance with missile characteristics and target threat.

The specific value of the constant c in Equation 12 for wn is generally determined for any particular missile by means of simulator analysis, values of c between 3.5 and 4.5 being farily common for typical modern missiles presently in use. The value of c, however, may assume any desired` form for presently existing or subsequently developed future missiles and, therefore, the variability of c-values provides for a wide range of adaptability. By way of example, a value of c=4 is chosen to illustrate the principles of operation of the programming computer of the instant invention in conjunction with the type A and type B programmed flight trajectories depicted in FlGS. 9 and l0 of the drawings.

is Setting c=4, the value of r becomes and the master Equation becomes 1 t=P en: 2ans -EWG n.2 edt-lconstant data to the second order computing circuit, and the value of the constant term in Equation 13.

Referring now to FIG. 7 of the drawings, which illustrates the novel second order computing circuit for a missile programmer, in accordance with the instant invention, and suitable for ready switching from a type A to a type B program, there is shown a second order computing circuit comprising a series of four amplifiers indicated as L 202, 203 and 204, respectively. Amplifiers 20E and 202 are conventional DC. analog type summing amplifiers, Well-known in the art and commercially available. Amplifiers 203 and 204 are conventional integrating arnplifiers. The input to amplifier 204 is c, the rst derivative of eo, the output of amplifier 204 being -eo. The latter qu-antity is directed to the output converter servo section 26 prior to transmission to the guidance transmitter 27 and is also simultaneously fed back as an additional input to amplifier 201 which receives the input data e1, the nature of which is determined by the desired tiight trajectory program. The input to amplifier 201 is thus ei-eo and the output, in view of the 180 phase shift which takes place in the amplifier 201 and the resulting reversal in sign, is therefore eO-ei or e. For purposes of solving Equation 13, the quantities one and @D26 must be obtained. The latter is accomplished as described below.

The output of amplifier 201, which is e, is fed to a potentiometer 205, the shaft position of which is equal in value to wn, the gain sensitivity factor. Hence, since the input to` potentiometer 205 is e, the output therefrom is equal to wn multiplied by e or one. The latter quantity is fed as an input to amplifier 202 and is also directed to a second potentiometer 206 whose shaft position likewise is adjusted to the value of un, the output from potentiometer 206 being onge which is fed directly as an input to integrating amplifier 203. The manner in which an output voltage proportional to wn is obtained to control the shaft positions of potentiometers 20S and 206, in accordance with Equation 12, will be subsequently described. For purposes of the instant discussion, it will suffice to say that wn is limited to values between zero and unity, in accordance with Equation 6, and since the shaft positions of both potentiometers 205 and 206 are at all times set to the value of wn, therefore the respective outputs from the latter potentiometers are functions of the input voltages across the potentiometers and directly proportional to wn. It is realized of course that the use of the second potentiometer 206 connected in the manner shown to obtain @n2 is merely a close approximation method since the effect of the second potentiometer 206 is to load the first potentiometer 205. Hence, to increase the accuracy of such an approximation approach, the second potentiometer 206 is supplied with a somewhat higher value of total resistance than that of the first potentiometer 20S.

It has been established that the input to amplifier 202 is one and the input to integrating amplifier 203 is wne. The gain of amplifier 202 is adjusted to provide a multiplication factor of two as well as the usual reversal in sign through inherent phase shift. Similarly, the gain of amplifier 203 is adjusted to provide multiplication by the factor a in Equation l0, which in our illustrative example 14 is set equal to one-half. Thus,`the output of amplifier 202 is equal to -Zwne whereas the output of integrating amplifier 203 is t=1 t G wn2edt+constant It will be noted that the sum of the outputs from amplifiers 202 and 203 is equal to the first derivative of eo, or o, in accordance with Equation 13. This being the case, the outputs of amplifier 202 and integrating amplifier 203 are fed directly to integrating amplifier 204, the gain of amplifier 204 being set to unity, to produce an output from amplifier 204 equal to -e0.

The preceding has been a discussion of the basic second order computing circuit utilized in the multiple flight course missile programmer of the instant invention. By varying the nature of the input data e1 to amplifier 201 and the value of the constant initially fed to integrating amplifier 203 prior to commencement of integration at the compute signal, the nature of the output ight trajectories represented by e0 can be molded to conform to either the type A or type B programs.

It should be noted that the second order computing circuit described above allows eo to gradually approach ei, until actual intercept with the target, in a manner and degree dependent upon the rapidity with which e0 can change, the latter being controlled by themagnitude of the gain sensitivity factor wn which controls the shaft settings of the `potentiometers 205 and 206. VIf wn is allowed to reach its maximum value of unity, when eo can approach e1 very rapidly since the feedback loop gain is very high, whereas if the wn settings of potentiometers 205 and 206 are near their lower limits, that is with on considerably less than unit, then the feedback loop gain is very low and eo will follow input data e1 rather slowly, and with a substantial lag. One purpose, therefore, of the second order programming computer is to cause eD to approach e1 from an initial value of e., and proceed through a transient midcourse phase whose nature and time duration is controlled by the manner in which the gain sensitivity Ifactor, wn, is programmed. As will be subsequently shown for the type A program, the accuracy with which EG-ET can follow DT-DM is determined by the net gain of the circuit in accordance with the value of on, a large value of wn increasing the tightness of following and reducing the transient error due to rapid variation in the input voltages. On the other hand, a low value of wn provides heavy smoothing of noisy radar data. In practice, therefore, t'ne manner of programming wn is a compromise between the supression of noise on the input data e1, to prevent vibration of the missile wing fiaps and subsequent increased drag and possible damage to the missile wing servos, and maximum probability of target kill. Thus, wn is programmed in time in such a manner as to enable e(J to follow e, to an extremely close tolerance as actual collision with the target approaches, that is, a large Value of wn is utilized to increase the tightness of following during the latter portion of the programmed flight trajectory when -the missile is close to the target, whereas a small value of wn is utilized for the initial portion of the programmed flight trajectory to provide heavy smoothing of noisy radar input data, thereby minimizing missile wing vibration, servo damage and air drag, and enhancing fuel economy.

The parameters necessary to achieve the desired program trajectories, type A and type B, will be next described. The desired shape of the type A and type B flight trajectories is evident from an examination of FIG. 10 of the drawings. In both programs the missile is fired at an initially high launcher elevation angle to enable the missile to reach maximum altitude as quickly as possible. The missile then cruises as long as practical at this altitude for maximum ramjet engine efiiciency and consequent fuel economy, and thereafter dives toward the target from above the latter. Referring to FIG. 9, it will be noted, however, that the manner in which EG-ET varies with time is significantly different for the ltype A and type B programs, the type A program involving a nearly linear direct intercept collision course to the target, whereas the type B flight trajectory provide for an asymtotic approach to the target.

Referrin" again to FIG. 7 of the drawings, the nature of the input parameters to amplifier 201 required to obtain the desired type A and type B programs are set out below.

For the type B program, the simpler of the two programs to be described, the input to amplifier 201 and the output from amplifier 204 for the elevation circuit (the azimuth circuit being controlled in substantially the same manner) is ei=ET and (14) eo=EGr The initial condition constant fed into integrating amplitier 263 and frozen at its value existing at guidance initiation is as previously set out in Equation 15, above.

The constant 2ans is conveniently obtained from the output of amplifier 2tlg?. before compute (guidance initiation) begins, after which the output of amplifier 262 is directed solely as an input to integrating amplifier 204.

wn may be expressed, in accordance with Equation 6, for c=4 as TPI-b4 A graph depicting the manner in which on is programmed in time for the type B program is shown in FIG. 11 of the drawing.

For the type A program, the necessary parameters -for the general system equation are found to be as follows:

The input to amplifier 2531 is to be range dependent -as Well as elevation dependent, in order to establish the direct nearly linear EG-ET type A program collision course shown in FlG. 9 of the drawings. Therefore,

As for the type i3 program, on and e0 are:

@PEG (19) and 4 20 a, TPI+4 lt will be further noted that for both the type A and type B programs an initial condition value is fed to integrating amplifier 2M prior to guidance initiation so that at guidance initiation the initial value of the output of amplifier 294 will be EGG which is the desired initial elevation angle of the guidance transmitter for capture of the missiie. Once the missile is captured, EGG is switched out of the circuit since there is no longer any need for it. The same procedure is followed in the .azimuth circuit.

`Referring now to FG, 7 .of the drawings, the term 16 K(DT-DM) in Equation 18 is determined as described below.

For the type A program, the output (e0-ei) from amplifier 201 is to be maintained equal to zero until guidance initiation and the latter is accomplished in the following manner.

The output of amplifier 281 is fed to a K servo 253 which positions the shaft of potentiometer 267, the latter having a voltage equal to DT-DM impressed across it, such that a null or zero output condition is maintained at the output of amplier 201. At guidance initiation, the K servo is locked by means of a brake 269, activated by the guidance signal, so that the scale factor constant K is maintained during the remainder of the flight program at the same value it has at guidance initiation.

Thus, the value of K is readily determined.

Q=Eoo ei=ETGiK(DTG*DMG) Therefore, substituting the values of eo and e, from Equations 22 into Equation 21 and solving for yields (EGG-Ero) +K(DTG-DMG) :0 (23) and t EGG*ETG i K=- 24 Dro- DMG Since e=0 at guidance initiation, the output of amplifier 292 for the A program at the compute signal is zero, and hence, the constant term in-Equation 13 is also zero for the type A liight program.

Although wn for the type A program theoretically is programmed in accordance with Equation 20, it has been found in actual practice that the introduction of the term K(DT-DM) as part of the input data e, causes e, to vary Very rapidly and, therefore, in order to prevent eo from lagging ei by too great a margin, a higher value of the gain sensitivity factor, can, for the initial portion of the type A program iiight trajectory than would be ordinarily vobtained by programming wn in accordance with Equation 20 is desired. Therefore, on is held constant at a higher value, of the order of magnitude of .1, until the latter value is reached by normal program ming in accordance with Equation 20, the latter condition occurring when TPI is in the range of 30`to 40 seconds. Thereafter, wn is programmed in accordance with Equation 20 just as for the type B program.

A Igraph depicting the manner in which en is programmed in time for the t e A ro ram is shown inV FlG. 1l of the drawings.

i It will be readily observed from the circuit diagrams shown in FIG. 7 of the drawings that the novel second order computing circuit shown allows for ready conversion from the type A mid-course guidance program to the typeB mid-course guidance program. The latter conversion is accomplished through operation of switch 210 which consists merely of removing the K(DT-DM) input from amplifier 201 and providing an input condition to amplifier 203 from the output of amplier 262 so that the first derivative of en, which constitutes the in- Yput to amplifier 264, is maintained at a zero null condition for the type B program until guidance initiation.

Referring now to FIG. 5 of the drawings, there is shown a schematic representation in block diagram form of a complete multiple fiight course second order programmer in accordance with the instant invention and which is ,suitable for ready conversion to either of the type A or type B guidance programs. The system is shown to comprise three basic sections,'the input` converter servo section 24, the programmer computing section 25, and an output converter servo section 26 which converts output information from the programmer computing section to suitable synchro form for utilization by the guidance transmitters 27. The input lconverter servo section 24 is provided with suitable inputs in synchro form for target traverse TV, target elevation ET, target train TN, and slant range diierence between the target and the missile DT-DM to converters 35, 36, 37 and 39, respectively. Also included in section 24 are means 37 and 38 to rellect the target traverse into the train plane to obtain a corrected true value of target azimuth AT. The output voltages from the input converter servo section 24 are target elevation, true target azimuth, slant range difference, and

slant range ratedifference IDT-DMI, all of these magnitudes being in D.C. voltage form for utilization by the programmer computing section 25. The quantities ET, AT, DT-DM and DT-DM are directed to their respective input ampliiiersdtl, 4l, and 42. The outputs of the elevation and azimuth input ampliliers itl and 41 are then fed through the wn circuitry section 47 to their respective elevation and azimuth integrating circuits 43 and 44. The output of the range and range rate input amplifiers 42 are directed to several portions of the computer section. Range difference is fed to the K constant servo sections 45 and 46 in the elevation and azimuth computing circuits as well as to the wn circuitry section 47. Range rate difference is fed to a suitable circuit 48 for obtaining multiplication of DT-`DM by the chosen value of the constant cf the resulting quantity being directed to the wn circuitry section 47. The outputs of the elevation and azimuth input ampliiers 4t) and 41 are also directed to the on circuitry section 47, wherein the required multiplication by wn and mm2 takes place andthe resultant quantities are then delivered to the elevation and azimuth integrators in sections 43 and 44, the outputs of which are EG and AG, respectively. The quantities EG and AG are then directed in D.C. voltage form to the output converter servo section 26 where they are reconverted into synchro signal form via converters 49 and 50 for transmission to the elevation and azimuth circuits 51 and 52, respectively, of the guidance transmitters27, whereby the latter guidance transmitters are commanded into proper position.

Referring now to the FIGS. 6 and 6a of the drawings, there is shown in greater detail the instrumentation and circuitry for a multiple flight course missile programmer suitable for carrying out the type A and type B program flight trajectories depicted in FIGS. 9 and 10 of the drawings. Essentially, as in FIG. V5, the programmer of the instant invention may be considered to comprise three main sections, that is an input data repeater section, a computer section and an output data repeater section. The irst section, the input data section is composed of iive servo data repeaters. `These are:

(l) target traverse (TV), (2) target elevation (ET), (3) target train (TN), (4) true target azimuth (AT) and (5) slant range difference between the target and the missile (DT-DM). This group of seu/os may be in itself subdivided into two classifications, that is, range diterence, and what is generally termed as the 3 to 2 coordinate converter sections. The range difference servo 'is to convert synchro data representing a three axis systein (TN, TV and ET) to D C. voltages representing a two axes system (ET and AT) for the programmer computing section. As stated previously, the true target azimuth AT is obtained in accordance with Equation l, the required information being obtained as described below. Y

Synchro data representative of the target traverse coordinate is fed to the TV servo 53 to position the servo motor 58 which operates a potentiometer 59, the voltage obtained from the slider arm of the potentiometer 59 being directly proportional to TV. The preceding is accomplished by feeding the Tv synchro signal from tracking radar 22 in FIG. l to a control transformer 6?, which isdesigned specilically to turn out a sizable voltage to a high impedance input such as that of an amplifier, the output of the control transformer '6% being fed to the servo amplifier 61 which provides sutiicient output torque and power to drive the servo motor 5S. The servomotor S8 in turn acts as a feedback device to position the rotor of the control transformer 66 in such a direction that the output of the control transformer 66 goes to zero, that is, the system performs as a nulling type of device wherein an error signal is fed back to the control transformer to reduce its output to zero, substantially in the same manner as the general servo system illustrated in FIG. 8 and previously described. At this point, the shaft position of the servo vmotor 58 isein the equilibrium state and is representative of the shaft position of the transmitting synchro at the tracking radar 22. The latter operation succeeds in getting the radar data into the traverse section in the form of a shaft position which is then readily converted to a D.C. voltage, for use in the computer section, by the servo motor driven slider arm 62 of the potentiometer 59. The latter potentiometer 59 is center tapped to ground and biased at each of its ends by positive and negative D C. voltages respectively, typical values of which may be i volts D.C. In the latter case, therefore, 100 volts D.C. would represent the desired number of degrees of traverse angle to be used as a standard, the voltage output from potentiometer 59 being directly proportional to some fractional portion of the latter standard. The elevation servo 54 operates substantially in the same manner as the traverse servo 53 in converting ET synchro data to D.C. voltage form. The ET synchro data is fed to a control transformer 63, the output of which is in turn directed to a servo amplifier 64. The output of the servo amplifier 64 is utilized to drive the servo motor 67 which in turn positions thevrotor of control transformer 63 and simulta- 'neously positions the slider arm 65 of a D.C. biased potentiometer 66. The elevation potentiometer 66 is shown grounded only at one end and, therefore, in the illustrated embodiment, provides onlyv positive values of elcvation. In addition to driving the slider arm 65, the servo motor 67 drives a secant calibrated potentiometer 68. The DC. voltage representing TV is directed from potentiometer 59 and applied across the secant function potentiometer 63. Since the position of the slider arm of potentiometer 68 is controlled by the ET servo motor 67, this type of arrangementwill produce at the slider arm of secant function potentiometer 68 a voltage equal to TV multiplied by the secant of ET, or T v sec ET. The secant potentiometer 68 may take any desired form well known in the art such as a shaped winding or specially loaded potentiometer or the like. The output voltage from the secant potentiometer 68 is fed as an input to servo amplifier 70 which positions servo motor 71. The latter motor '71 in turn controls the magnitude of a feedback voltage from the potentiometer 69 for input to servo amplifier itl to produce a null. The output shaft position of the motor 71, for a null condition in servo amplifier 7i), is proportional to TV sec ET. The output of the Tv sec ET servo motor 71 also drives the rotor of a dierential generator 72, which is an addition-type synchro, while synchro data representing target train, TN, is fed from the tracking radar 22 to the stator windings. of the differential generator 72. The output from the differential generator 72 is thus TN-l-TV sec ET which, in accordance with Equation l, isthe true value of target azimuth, AT, in synchro form.

The latter synchro output from the differential gen` is erator 72 is then fed to the AT servo section 56 wherein the servo motor 73 positions the slider arm 74 of a D.C. biased potentiometer 75' to produce a D.C. voltage output directly proportional to the target azimuth AT, in the same manner in which the elevation of the target ET `is derived in servo section 54 described above.

Information in synchro form relating to DT, for the type B program trajectory, or DT-DM, for the type A program trajectory, is directed as input to control transformer 76 of the range servo section 57, the servo motor 78 and servo amplifier 77 providing the necessary follow up error signal to control transformer 76. The servo motor 78 simultaneously controls the slider arm position of a negatively biased potentiometer 79 whose DE. output voltage is proportional to (DT-DM). Motor 78 is also used to position a differential device 81, the shaft position of which is used to similarly position a negatively biased potentiometer 80 whose D C. voltage output is proportional to -(DT-DM), the slant range rate difference. The shaft position of the differential device S1 controls a ball and disc integrator device 62 whose output shaft position is proportional to the integral of the first derivative of (DT-DM). The latter quantity is fed back as an error signal input to the differential converter 81 to establishV a null equilibrium, at which point the out put shaft position of the differential converter is proportional to the first derivative of DT-DM or, in other words, T-M- Thus, the differential converter 81 is a rnechanical differential device in which the derivative of the input is integrated and then fed back as an additional input to the differential device in the conventional servo error signal follow up procedure to establish a null state.

The two potentiometers 79 and 80 are both biased negatively to compensate for anticipated phase reversals to be effected in subsequent computer amplifiers within the programmer computing section.

In accordance with the above discussion sufficient D.C. voltages are now available as output from the input converter servo section 24 to facilitate operation of the programmer computer section 25 for either the type A or type B programs. These are D C. voltages proportional ET, AT, and either DT and DT for the type B program or DT-DM and DT-DM for the type A program. It is desired to act upon these voltages in the cornputer section in accordance with the prescribed matheniatical equations to produce output values of EG and AG for commanding the guidance transmitters 27 into proper position for guiding a missile in accordance` with the desired midcourse fiight trajectory programs.

The range difference voltage DT-DM is fed with a negative polarity from potentiometer 79 to the input of amplifier 101 and the range rate difference voltage T-DM is similarly directed from potentiometer 80 as input to amplifier 102. The latter amplifiers 101 and 102 have dual purposes, namely to minimize the loading effects on potentiometers 79 and 80, that is, to act as isolation amplifiers, and secondly to reverse the polarities of their respective input voltages, the latter being accomplished through the inherent 180 phase shifts which take place in these amplifiers. The range difference voltage DTT-DM is then fed from the output of amplifier 101 across the potentiometer 83, the slider arm of which is positioned by the KE elevation servo 84. From the potentiometer 83 a voltage equal to KE(DT-DM) is obtained and directed as a type A program input to amplifier 105. Also fed to amplifier 105 is a D.C. voltage proportional to target elevation ET and a negative D.C. feedback voltage representing elevation angle of the guidance transmitter, -EG, from the output of amplifier 109 in FIG. 6a.

ln the same manner as for the elevation circuit just described, Dry-DM is fed from the output of amplifier 101 to potentiometer 86 in the KA servo section 85, and amplifier 106 receives a type A program input equal Eff to KA(DT-DM). YAmplifier 106 also receives as input an AT signal from potentiometer '75 in the input con verter `servo section 24 and a feedback voltage representing :AG from the output of amplifier 112 in FIG. 6a. The azimuth portions of the novel programmer computing circuit embodiment ,described are thus essentially identical to the elevation sections with the exception that elevation is limited to values in one direction from zero, whereas azimuth is lai-directional about zero and may assume either plus or minus values about that point. Hence, it will be noted that the output of amplifier 101 is fed to one end of the KA potentiometer 86 and also to amplifier 104 Where its polarity is reversed and then fed to the other side of the KA potentiometer, the reason for the latter being obvious in view of the bi-direetional nature of azimuth values. Therefore, any of the remaining discussion hereinbelow pertaining to the elevation portions of the programmer circuitry of the instant invention are equally applicable to the azimuth sections.

Referring now aga-in to the KE servo section, it will be observed that .the KE servo Sri is positioned by the output of amplifier 105 such that the KE servo Will tend to maintain a value of KE(DT-DM) such that there is zero output from amplifier 105 as long as the two switches 87 and SS are closed. For the type A program, therefore, both switches 87 and 88 remain closed between the time of firing of the missile and the time when the missile is Icaptured by the guidance beam of the guidance transmitter Z7. At the time of capture of the missile by the guidance beam, the electrical input to the KE servo S4 is discontinued by opening switch S7 and the servo is simul taneously locked in position by means of a brake 39, actu-k Y ated by the guidance signal, to prevent'any erroneous movement of the sliderarm of potentiometer S3 after capture of the missile by the guidance beam. Thus, after guidance initiation, KE is held constant While the value of the input voltage to amplifier 105, KE(DT-DM), varies directly as the value of the slant range difference Dry-DM. The latter insures for the type A program that the angular difference between ET and EG will reach zero at the same time that the range difference VDT--DM equals zero. This constitutes the primary distinction between the type A and the type B programs since for the type A program the input is whereas for the type B program the input voltage is merely ET-EG. t

The output voltage DT-DM from amplifier 101 is also fed as one input to amplifier 103. The output of amplifier 102 is a DC. voltage proportional to the positive value of the first derivative of DT-DM, that is DT-DM, and is fed to a potentiometer 90 whose slider arm position is set by means of a hand crank 91 to the desired value of the constant c in Equation l2. The output from potentiometer 90, which represents c(DT-DM), is then fed as.

a second input to the summing amplifier 103. The output from amplifier 103 is, therefore, the sum of the input voltages .DT-DM and c(DT-DM) which is fed across potentiometer 92 as the denominator of the expression for wn previously set forth in Equation 12. The value of c(DT-DM) from potentiometer 9i? is simultaneously fed as input to the servo amplifier 93 of the wn division servo section. The output of servo amplifier 93 drives the servo motor 9K1 which, in turn, positions the slider arm 95 of the potentiometer 92. The output of the latter provides a feedback follow up voltage as a second input to the servo amplifier 93, such that the null equilibrium position of the slider arm 9S, as positioned by servo motor 94, is equal to wn as set forth in Equation 12. The servo motor 94 simultaneously positions the slider arms on potentiometers 96 and 97 in the second order computing section of the elevation circuit and potentiometers 93 and 99 in the second order computing section of the azimuth circuit.

The performance of amplifiers 107, 108 and 109 of the elevation circuit and ampliers 110,111, and 112, of the azimuth circuit are identical in operation to amplifiers 202, 203 and 204, respectively, of the second order computing circuit previously described in connection with FIG. 7 of the drawings. Therefore, prior to guidance, or before compute begins, the output of amplifier 107 sets the initial conditions CE upon integrating amplifier 108 and, after compute begins, the output of amplifier 107 is removed from amplifier 108 and applied solely as input to integrating amplifier 109. Similarly, the output of amplifier 110 of the azimuth circuit sets the initial conditions CA upon integrating amplier 111, prior to compute or guidance initiation, and thereafter is utilized solely as input to amplifier 112.

It is further pointed out that, in connection with the type A program, servo amplifier 93 receives'an wn: 0.1 signal and is locked in this state for a prescribed period of time of the order of Tplequals 30 to 40 seconds. The reason, as previously stated, for manipulating wn in this manner is to strike a suitable compromise between keeping down noise in the missile wing servos balanced against desirable close tracking of the target. To accomplish the latter, therefore, wn is initially held low lat a value of 0.1 -until the missile is within approximately 36 seconds of intercepting the target, at which point wn is allowed to approach unity as the missile nears the target since the increased guidance sensitivity enabled thereby allows the missile to maneuver much more readily in following the target closely.

Amplifier 109 receives an initial condition signal EGG which is not equal to ET but is considerably greater in elevation value and is computed by a suitable launcher computing section (not shown) which considers maximum guidance beam capture probability. Consequently, EGG is generally of the order of 20 to 30 greater than ET at guidance initiation and, therefore, the missile must be programmed downward onto the target. in a similar manner, the initial value of AGG is fed, prior to guidance initiation, into integrating amplifier 112. Once the missile has been captured by the guidance beam, the initial values of EGG and AGG are switched out of the circuit. Thus, EG is initially greater than ET and EG approaches ET as a transient phenomenon. The rate of change of EG is initially rather slow and gradually increases to a maximum rate of change as the missile nears the target, the rate of approach of EG-ET to zero being controlled by the value of on.

The outputs of amplifiers 109 and 112 are directed as feedback voltages to amplifiers 105 and 106, respectively. The output of amplifier 109 is also fed as input to the EG output converter servo section 49, the output of ampliiier 112 being similarly fed as input to the AG output converter servo section 50. These servos convert the D.C. output voltages EG and AG from amplifiers 109 and 112, respectively, to shaft positions for commanding the guidance radar transmitters 27 into proper position. The description of the output converter servo section 49 for the elevation circuit will be considered as illustrative. The D.C. voltage -EG is fed as input to servo amplifier 11?, the output of which drives servo motor 114 whose shaft position in turn controls the slider arm of a D C. biased potentiometer 115 to provide a follow up voltage for the servo amplifier 113. The servo motor 114 also drives a synchro generator 116 which in turn feeds synchro output for transmission to a control transformer 117, whose physical location is generally on the guidance transmitter itself. In accordance with conventional procedures, the output of control transformer 117 is then fed into a servo amplifier 118 which drives a servo motor 119 to provide both the follow up rotation for the control transformer 117 and simultaneously position the guidance radar 27. In this manner, the guidance radar 27 follows the command signal and is aimed at the computed value of the elevation angle EG. The azimuth output converter servo section 50 performs in substantially the same manner as the elevation circuit. The outputs of the synchro generators 116 and 120 in the elevation and azimuth circuits are not only utilized to transmit synchro data over long distances to the guidance transmitters 27, but also direct their output to a data box 121 the sole function of which is to record the values of elevation and azimuth guidance signal output.

The novel multiple iiight course missile programmer of the instant invention therefore provides extremely wide adaptability'to a great variety of flight trajectories desired for use in conjunction with specic missiles and target considerations. Although illustrated for the type A program and the simpler type B program, the second order programming computer of the instant invention may be made dependent upon any set of input parameters and will consistently act upon the latter in the same manner, irrespective of their nature, to cause such parameters to approach desired values in accordance with the generalized system equations previously set out and which are readily tailored to fit the requirements of any specific trajectory. Midcourse flight trajectories thus provided offer an ideal compromise between maximum fuel economy, maximum missile range and maximum probability of target kill on the one hand, and adequate smoothing of noisy radar data on the other.

Obviously, many modifications and variations of the present invention are possible in 'the light of the above teachings. It is therefore to be understood, that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described.

Having thus described the invention, what is claimed 1. Apparatus for controlling the flight course of a guided missile to its target comprising in combination a search radar, tracking radar means for .tracking a target in accordance with target azimuth, target elevation and selectable target range data received from said search radar, guidance computer means for acting upon tracking radar output information relating to target traverse, target elevation, target train and slant range difference between the target and the missile, guidance radar means for guiding the missile in accordance with a prescribed trajectory, means to command said guidance radar into position in accordance with output azimuth and elevation signals from said guidance computer means, receiving means on said guidance radar for receiving a signal from said missile proportional to missile range, and means for selectably directing said missile range signal from said guidance radar to said tracking radar means to enable said tracking radar means to produce an output ysignal proportional to slant range difference between the target and missile for said guidance computer means.

2. Apparatus for controlling the flight lcourse of a guided missile as set forth in claim l wherein said guidance computer means comprises an input converter servo section, a programmer computing section, and an output converter servo section, said input converter servo section including means to convert input synchro signals relating to vtarget traverse, target elevation, target train and slant range difference between the target and the missile to D.C. voltages proportional to target elevation, true target azimuth, slant range difference between the target and the missile and slant range rate difference between the target and the missile, said programmer cornputing section including elevation and azimuth input amplifiers for receiving respectively said target elevation and true target azimuth Voltage signals from said input converter section, computer means performing addition, amplification, function generating and integration steps responsive to the respective output signals from said elevation and azimuth amplifiers for acting upon said output signals in accordance with prescribed program flight equations to produce output voltage signals proportional to guidance transmitter elevation and azimuth, means to vary the magnitude of the input voltages to said amplifier and integration circuits as a function of a quantity which is itself a function of slant range difference and slant range rate difference, means to feed back said signals proportional to guidance transmitter elevation and azimuth respectively to the inputs of said elevation and azimuth input amplifiers, means to provide additional input signals respectively to said elevation and azimuth input amplifiers such that the outputs of said input amplifiers are-maintained :at zero levels until the missile is captured by the guidance ybeam of the guidance transmitter, and means to thereafter vary said additional input signals solely in proportion to the product of slant range difierence and -a constant, said output converter servo section including means to convert the D.C. output signals proportional to guidance transmitter elevation and azimuth to synchro signal form for transmission to said guidance transmitter.

3. Apparatus for controlling the fiight course of a guided missile to its target comprising in combination tracking radar means for tracking a target and obtaining target position information, a missile fiight trajectory guidance computer, means at said computer for acting upon tracking radar :target position output data, guidance radar means for guiding the missile in accordance with the prescribed trajectory, means to command said guidance radar means into position in accordance With output azimuth and elevation signals from said guidance computer means, receiving means on said guidance radar for selectably receiving a signal from said missile proportional to range from the guidance radar to the missile, and means for directing said missile range signal from said guidance radar means to said tracking radar means.

4. In an apparatus for controlling the flight course of a guided missile in conjunction with a guidance transmitter, guidance computer means comprising an input section, a programmer fiight trajectory computing section, and an output section, said input section including means to convert input synchro signals to D.C. voltage form for use in said programmer computing section, said programmer computing section including input amplifiers for receiving said D.C. voltage signals from said input section, amplifier and integration circuit means operably connected to and responsive to the respective output signals from said input amplifiers for acting upon said output signals in accordance with prescribed program ight trajectory equations to produce output voltage signals proportional to desired guidance transmitter positions, means to vary the magnitude of the voltage inputs to said amplifier and integration circuit means as a function of slant range difference between the target and the missile and slant range rate difference, means to feed back said output signals proportional to guidance transmitter positions to the inputs of said input amplifiers, means to provide additional input signals to said input amplifiers such that the outputs of said input amplifiers are maintained at zerolevels until the missile is captured by the guidance beam of the guidance transmitter, and means to thereafter vary said additional input signals Vsolely in proportion to the product of a single varying parameter and a const-ant, said output section including means to convert the D.C. output voltage signals proportional to guidance transmitter positions to synchro signal form for transmission to said guidance transmitter.

5. In an apparatus for controlling the flight course of a guided missile in conjunction with a guidance transmitter, guidance computer means comprising an input converter section, a programmer computer section, and an output converter section, said input section including means to convert input synchro signals to D.C. voltage form for use in said programmer computing section, said programmer computing section including input amplifiers for receiving said DC. voltage signals from said input converter section, amplifier' and integration circuit meansbeing where TPI is the time remaining until intercept of the target by the missile, and c is a constant,

means to feed back said output signals proportional to guidance transmitter positions to the inputs of said input Y amplifiers, said output converter section including means to convert the DC. output voltage signals proportional to guidance transmitter positions to synchro signal form for transmission to said guidance transmitter.

6. The apparatus of claim 5 wherein the Value of c is between 3.5 and 4.5.

7. The apparatus of claim 5 inciuding means to provide additional input signals to said input amplifiers such that the outputs of said input amplifiers are maintained at zero levels until the missile is captured by the guidance beam of the guidance transmitter, and means to thereafter vary said additional input signals solely in proportion to the productl of a single varying parameter and a constant.

8. The apparatus of claim 7 including means to prevent the value of the gain sensitivity factor wn from decreasing below a prescribed minimum value.

9. The apparatus of claim 8 wherein value for wn is 0.1.

l0. Apparatus for controlling the flight course of a guided missile to a target comprising a guidance computer and a source of DC. voltage signals relating to target position data for use by said guidance computer, said computer including input amplifiers for receiving said DC. voltage signals, amplifier and integration circuit means being electrically coupled, said amplifier and integration circuit means coupled to said input amplifier and responsive to the respective output signals from said input amplifiers for acting upon said output signals in accordance with the relations the minimum and where el, is the output data from said computer,

ci is the input data to said computer,

0'0 is the first derivative of e0,

wn is the gain sensitivity factor of the computer, a is a constant,

P is the present time, and

G is the time of guidance initiation,

to produce output voltage signals proportional to desired guidance ytransmitter positions, means to Vary the magnitude of the computer gain sensitivity factor wn in accordance with the relation i Where TPI is the time remaining until intercept of the target ny the missiie, and c is a constant,

25 and means to feed back the D.C. output signals from said computer to the inputs of said input amplifiers.

11. The apparatus of claim wherein the value of c is between 3.5 and 4.5.

12. The apparatus of claim 10 including means to provide additional input signals to said input ampliers such that the outputs of said input amplifiers are maintained at Zero levels until the missile is captured by the guidance beam of the guidance transmitter, and means to thereafter vary said additional input signals solely in proportion to the product of a single varying parameter and a constant.

13. The apparatus of claim 12 including means to prevent the value of the gain sensitivity factor wn from decreasing below a prescribed minimum value.

14. The apparatus of claim 13 wherein the minimum value for wn is 0.1.

15. Apparatus for controlling the flight trajectory of a missile to its target comprising a computer, means to supply input voltages to said computer proportional to target elevation, target azimuth, and slant range ditference between the target and the missile, means to vary the latter parameters in accordance with the equations and means to vary the gain sensitivity factor wn of the computer in accordance with range difference and range rate difference.

16. Apparatus for controlling the flight trajectory of a missile to its target comprising a computer, means to supply input voltages to said computer, means to vary the input parameters to said computer in accordance with the equations t=1 e=ft=G eodt t=1 0: 2w (euci) aft G an? (eoei) dt-iconstant and where eo is the output data from said computer,

e, is the input data to said computer,

do is the first derivative of e0,

wn is the gain sensitivity factor of the computer, ois a constant,

P is the present time, and

G is the time of guidance initiation,

means to vary the gain sensivity factor w,1 of the computer in accordance with range difference and range rate diiference, and means to feed back the output of said` computer to its input.

17. Apparatus for controlling the flight trajectory of a guided missile to its target comprising a computer, means to supply input voltages to said computer proportional to target elevation, target azimuth, and slant range difference between the target and the missile, means to la@ vary the latter parameters in accordance with the equations and eo is the output data from said computer,

ei is the input data to said computer,

e'o is the first derivative of e0,

wn is the gain sensitivity factor of the computer, a is a constant,

P is the present time, and

G is the time of guidance initiation,

means to feed back the output voltages of said. computer to its input, and means delaying maximum gain sensitivity of said computing circuit until the missile is close to the target, whereby noisy input radar data is smoothed until maximum maneuverability of the missile is required.

18. Apparatus for controlling the night trajectory of a missile to its target in conjunction with a guidance transmitter comprising a Computer, means to supply D.C. input voltages to said computer proportional respectively to target elevation, target azimuth, and slant range difference between the target and the missile, means to vary the latter parameters so that the azimuth of the guidance transmitter approaches the azimuth of the target and the elevation of the guidance transmitter approaches the elevation of the target in the same manner as the missile range approaches the target range in accordance with equations and t=P e0= -Zwn (eoei) afVG wuz (eoei) dt-lconstant where eo is the output data from said computer,

e, is the input data to said computer,

o is the first derivative of e0,

wn is the gain sensitivity factor of the computer, ais a constant,

P is the present time, and

G is the time of guidance initiation,

References Cited by the Examiner UNITED STATES PATENTS s/57 'winiams et al. 244-14 OTHER REFERENCES Radar Guided Missiles, Wireless World, February 195 6, pp. 67-70.

SAMUEL FEINBERG, Primary Examiner.

FREDERICK M. STRADER, CHESTER L. JUSTUS,

Examiners. 

3. APPARATUS FOR CONTROLLING THE FLIGHT COURSE OF A GUIDED MISSILE TO ITS TARGET COMPRISING IN COMBINATION TRACKING RADAR MEANS FOR TRACKING A TARGET AND OBTAINING TARGET POSITION INFORMATION, A MISSILE FLIGHT TRAJECTORY GUIDANCE COMPUTER, MEANS AT SAID COMPUTER FOR ACTING UPON TRACKING RADAR TARGET POSITION OUTPUT DATA, GUIDANCE RADAR MEANS FOR GUIDING THE MISSILE IN ACCORDANCE WITH THE PRESCRIBED TRAJECTORY, MEANS TO COMMAND SAID GUIDANCE RADAR MEANS INTO POSITION IN ACCORDANCE WITH OUTPUT AZIMUTH AND ELEVATION SIGNALS FROM SAID GUIDANCE COMPUTER MEANS, RECEIVING MEANS ON SAID GUIDANCE RADAR FOR SELECTABLY RECEIVING A SIGNAL FROM SAID MISSILE PROPORTIONAL TO RANGE FROM THE GUIDANCE RADAR TO THE MISSILE, AND MEANS FOR DIRECTING SAID MISSILE RANGE SIGNAL FROM SAID GUIDANCE RADAR MEANS TO SAID TRACKING RADAR MEANS. 